Key Processes involved

Make a conjecture (an example is or is not
impossible) and then seek to justify it; work
logically towards a solution, recognising the
impact of the constraints involved

Interpreting and evaluating

Form convincing arguments, and formulate proofs

Communicating and reflecting

Communicate reasoning and findings effectively

Teacher guidance

You could begin by showing slide 1. Cross 2 off the
list and write it in, at the top of the puzzle. Then
make the following points:

I want to find a way to place the
seven numbers in the boxes

so that each straight line adds up to the same total.

This is called the magic sum.

I am only allowed to use each number 1
to 7 once in the puzzle.

Now, complete the puzzle as shown, silently,

without telling pupils how you did it.

Does this work? What is the magic sum?
How can you tell?

Slide 2 provides an alternative starting point. The
content and range in this task are low, requiring only
the use of properties of integers (e.g. even or odd) to
make generalisations. There is also an opportunity to
construct, express in symbolic form, and use simple
formulae when formulating the proof.